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Tentukan polinomial p ( x ) dan q ( x ) dengan ketentuan berikut. a. dan berderajat 4 dengan syarat p ( x ) + q ( x ) berderajat 3.

Tentukan polinomial  dan  dengan ketentuan berikut.

a. undefined dan undefined berderajat 4 dengan syarat  berderajat 3.

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A. Adalah

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polinomial dan .

polinomial undefined dan undefined.

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Misal: Contoh: Misal dan . Jadi, polinomial dan .

Misal:

 begin mathsize 14px style p left parenthesis x right parenthesis equals a x to the power of 4 plus b x cubed plus c x squared plus d x plus e q open parentheses x close parentheses equals negative a x to the power of 4 plus b x cubed plus c x squared plus d x plus e end style 

  begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell p open parentheses x close parentheses plus q open parentheses x close parentheses end cell equals cell open parentheses a x to the power of 4 plus b x cubed plus c x squared plus d x plus e close parentheses plus left parenthesis negative a x to the power of 4 plus b x cubed plus c x squared plus d x plus e right parenthesis end cell row blank equals cell a x to the power of 4 minus a x to the power of 4 plus b x cubed plus b x cubed plus c x squared plus c x squared plus d x plus d x plus e plus e end cell row blank equals cell 2 b x cubed plus 2 c x squared plus 2 d x plus 2 e end cell end table end style 

Contoh:

Misal begin mathsize 14px style p left parenthesis x right parenthesis equals x to the power of 4 plus x cubed plus x squared plus x plus 1 end style dan begin mathsize 14px style q left parenthesis x right parenthesis equals negative x to the power of 4 plus x cubed plus x squared plus x plus 2 end style.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell p left parenthesis x right parenthesis plus q left parenthesis x right parenthesis end cell equals cell left parenthesis x to the power of 4 plus x cubed plus x squared plus x plus 1 blank right parenthesis plus left parenthesis negative x to the power of 4 plus x cubed plus x squared plus x plus 2 right parenthesis end cell row blank equals cell x to the power of 4 minus x to the power of 4 plus x cubed plus x cubed plus x squared plus x squared plus x plus x plus 1 plus 2 end cell row blank equals cell 2 x cubed plus 2 x squared plus 2 x plus 3 end cell row blank blank blank end table end style   

Jadi, polinomial undefined dan undefined.

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Diketahuipolinomial f ( x ) = x 2 − 4 x + 2 dan g ( x ) = x 3 − 3 x 2 − 2 x + 1 . Jika h ( x ) = 2 f 2 ( x ) − f ( x ) × g ( x ) , tentukan: b. derajat polinomial h ( x ) ; dan

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